Application of biconjugate gradient stabilized method with spectral acceleration for propagation over terrain profiles

Abstract

Using the Method of Moments (MoM) for the computation of electromagnetic radiation / surface scattering problems is a very popular approach since obtained results are accurate and reliable. But the memory requirement in the MoM to solve discretized integral equations and the long computational time of O(N3 ) operation count (where N is the number of the surface unknowns) make the method less favorable when electrically large geometries are of interest. This limitation can be overcome by using BiConjugate Gradient Stabilized (BiCGSTAB) method, a non-stationary iterative technique that was developed to solve general asymmetric/non-Hermitian systems with an operational cost of O(N2 ) per iteration. Furthermore, the computational time can be improved by the spectral acceleration (SA) algorithm which can be applied in any iterative technique. In this thesis, Spectrally Accelerated BiCGSTAB (SA-BiCGSTAB) method is processed over systems that have huge number of unknowns resulting a computational cost and memory requirement of O(N) per iteration. Applications are presented on electrically large rough terrain profiles. The accuracy of the method is compared with MoM, conventional BiCGSTAB method and Spectrally Accelerated Forward-Backward Method (SA-FBM) where available.